What Is the Probability of Finding an Electron at the Center of a Quantum Well?

[kwuk]

Hi, I have been given the following problem;

If an electron is confined to a 1-D potential well of infinite barrier height and width
L, the normalized wavefunction Psi(x) of the electron in the various quantized states, n,
is given as Psi_n(x)=(2/L)^0.5 sin(n pi x / L).

For the n=2 state, what is the probability of finding the electron at the centre of the
well?


I have calculated these probability questions in the past, but they have always been for a probability across a range of values for x, i.e from 0 to L/2, which I use as my limits when integrating. In this case however, it is asking about a specific point. I assume that the answer is zero, as the upper and lower limit are identical. Is this correct?

Thanks.

 

[vela]

Yes, with a continuous probability distribution, the probability of a obtaining a specific number is always 0. It's only meaningful to talk about the probability of finding the random variable in some range of values.

I think it was just a poorly worded question. The problem likely wants you to find the probability of finding the particle between x=L/2 and x=L/2+dx.